Lucky Pool
There are four friends, Andrea, Barbara, Clara, and Diana, all of whom share the same birthday. They've decided to trade gifts with one another such that no girl receives her own purchase and no girl knows the identity of the buyer of the gift she receives.
Then the 4 gifts turn out to be a book, a coupon, a dress, and a mug, and the following information is additionally revealed to all of them:
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Andrea bought a dress but didn't receive a mug.
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Barbara received a mug but didn't buy a coupon.
Diana then truthfully claims that she knows the item that everyone bought, but she can't exactly match each item to its receiver.
What item did Diana receive?
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1 solution
"Diana then truthfully claims that she knows the item that everyone bought, but she CAN'T exactly match each item to its receiver."
B got a mug and bought a book.
A bought a dress and received either a book or a coupon.
C and D bought a mug and a coupon together between themselves.
If Diana didn't get Andrea's dress, that means she got either a book or a coupon, same as Andrea, so it must be that she CAN know who received what (in which Andrea got whatever Diana didn't, and of course she'd know what she received herself (duh!), and with Barbara getting a mug made public then Clara can only get the dress that none of the others had).
So it should be Diana who's getting that dress if she can't tell the receivers apart.
OR